An airline flies a daily flight from City A to City B. Currently they sell each ticket for $600, and on average 600 people take the flight, so their revenue per flight is $180,000.

Question

They are interested in seeing whether they can increase their revenue by changing the price of a ticket. Based on market research they discover that for every $ 4 increase in ticket price, one fewer person will buy a ticket. Similarly for every $4 decrease in ticket price, one more person will buy a ticket. What ticket price would maximize the airline’s revenue?

Answer 1

P=$600

at $600

x passengers buy round trip tickets

x=600

one way trip Revenue =R = .5(600)(600)=180,000

at P=604, x=599, R=.5Px= .5(604)(599)

x=-(P-600)/4 +600=-P/4+750

R=.5Px

R= -P^2/8 +375P

R' =-P/4+375=0

P=$1500=revenue maximizing Price

x=375

Px=R= 375(1500)= $562,500= max Revenue